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Europhysics Letters (EPL)

From continuous Wigner function to discrete Wigner function

Tomer Bar-On

Published Oct 1, 2009• 5 citations
Publisher

Abstract

We construct a version of the discrete Wigner function (DWF) for any dimension. This DWF will be constructed from the continuous Wigner function (CWF). In addition, this DWF has many properties of the CWF.
DOI
10.1209/0295-5075/88/10002

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We observe that the discrete Wigner functions (DWFs) of n-partite systems with odd local dimensions are tomographically universal, as reflected in the delta function form of the DWF for any stabilizer. However, in the n-qubit case, this property does not hold due to the non-factorization of the mapping kernel, the explicit form of which depends on a particular partition of the discrete phase space. Nonetheless, it turns out that the DWF for some specific stabilizers, not included in the set used for the construction of the Wigner map, takes on the form of a delta function. This implies that the possibility of classical simulations of Pauli measurements in a given stabilizer state for qubit systems is closely tied to the experimental setup.